Answer to Question #11530 Submitted to "Ask the Experts"

We have a thorium dioxide (ThO₂) quantitative microanalysis standard that is 1.6 mm by 1.6 mm in size. I've read that thorium produces mostly alpha particles, but I also recently read that thorium decays to many daughter radionuclides that generate beta and gamma rays.

Does ThO₂ produce beta and gamma rays? If so, is there software available that can estimate the amount of beta and gamma radiation produced over time?

Thorium-232 (²³²Th) is present in significant amounts in the Earth's crust and is an alpha-emitting radionuclide, which decays to radium-228 (²²⁸Ra), which is a beta emitter with a half-life of about six years; it emits no significant gamma radiation. The ²²⁸Ra ultimately decays through multiple radioactive progeny, four others of which decay by beta emission with the associated emission of various gamma rays, to stable lead-208 (²⁰⁸Pb). So, yes, the decay of thorium through its radioactive progeny does produce significant gamma and beta radiation.

You can find a large number of graphical and tabular displays of the ²³²Th decay chain on the internet. Here is a link to one that shows the decay chain with decay modes and half-lives for all the radionuclides and some gamma emission information for a major radionuclide in the chain (thallium-208 [²⁰⁸Tl]). Here is a second link to a Brookhaven National Laboratory site that allows you to see all the radiations of possible concern associated with the decay of any radionuclide. Enter the identity, e.g. Ac-228, of any progeny of interest and all the pertinent decay data will be displayed. If you wish you may restrict the types and/or energies of radiations displayed by selecting from the appropriate boxes.

The yields shown represent the fractional yield of the particular radiation per disintegration of the radionuclide. If sufficient time has passed since the separation of the ²³²Th from other materials then secular equilibrium may exist between the progeny and the parent thorium. "Sufficient time" here means that roughly seven half-lives of the longest-lived progeny, ²²⁸Ra, have passed, implying an elapsed time of about 40 years. In this time, under a secular equilibrium condition, the ²²⁸Ra and all subsequent progeny that are not produced through a branch decay (one of two or more alternative decay routes) of a precursor radionuclide would have the same activity as that of the long-lived parent, ²³²Th. The progeny, polonium-212 (²¹²Po) and ²⁰⁸Tl, are produced in respective yields of about 0.64 and 0.36 from the branch decay of bismuth-212 (²¹²Bi). Therefore, under secular equilibrium conditions, these two radionuclides would have respective activities equal to 0.64 and 0.36 of the activity of the chain parent ²³²Th.

If considerably less time than 40 years has passed since the thorium in your source was separated from its progeny, the decay progeny would not be in secular equilibrium, and you could not make the above simple assumptions regarding relative activities. The linear first-order kinetics that govern the decay processes are well known and analytical solutions for any progeny member in a series decay can be determined. The original equations that show how the progeny activities are related to the chain parent and to each other are credited to Bateman, and you can find many references to him and his results by searching the Internet.

Many people have devised simple computer programs to solve the equations. A convenient and effective calculator program is available at the Uranium Wise site. Type "Th-232" (without the quotation marks) in the first chart in the "Series Name" box, accept "Th-232" for the "Nuclide Name," specify a nominal activity for the ²³²Th, and select "Pure" as the state of the ²³²Th (i.e., no progeny present). Then specify a start and stop elapsed time in the second chart, select "line chart" in the "Chart Type" box, select "all individual nuclide activities" in the "Chart Detail" box, and leave the "Chart Axes" box set for the log-log display. Click "Calculate" below the chart, and you will see the results for each of the expected activities for all members of the chain along with the decay/ingrowth curves for each member of the series. It is then a simple matter to get the expected beta and gamma emission rates for specific-energy beta particles and specific-energy photons from a specific radionuclide in the chain by multiplying the activity by the respective beta yield or gamma yield for the radionuclide of interest. The calculating software also allows the user to change various parameters to see how they affect the results.

George Chabot, PhD